Q1Wireless Communication

FHSS: Basic Block Diagram and Processing Gain in Fast and Slow Systems

In Frequency Hopping Spread Spectrum, the data stream is first modulated (typically using FSK or another simple modulation) onto an intermediate-frequency carrier, and this modulated IF signal is then mixed with a locally-generated frequency synthesizer output whose instantaneous frequency is controlled by a pseudo-noise code generator, causing the transmitted RF carrier to 'hop' rapidly among a large set of discrete frequency channels spanning the total available spread bandwidth, following a pseudo-random hopping pattern known to both transmitter and receiver. At the receiver, an identical, precisely synchronized PN-driven frequency synthesizer drives a corresponding dehopping mixer that translates the hopping received signal back to a fixed IF frequency, after which conventional demodulation recovers the original data.

FHSS systems are classified as either slow-hopping or fast-hopping, depending on the relationship between the hop rate Rh (hops per second) and the data symbol rate Rs (symbols per second). In a slow FHSS system, multiple data symbols (or bits) are transmitted during each single frequency hop (Rh < Rs, i.e., the hop duration Th spans several symbol periods Ts), so the hop rate is lower than the symbol rate. In a fast FHSS system, the hopping is faster than the data symbol rate (Rh > Rs, i.e., multiple frequency hops occur within the duration of a single data symbol), meaning each symbol is actually transmitted as several sub-hops, providing additional frequency diversity per symbol at the cost of a higher hop rate and correspondingly higher synthesizer switching-speed requirements.

For an FHSS system, the processing gain Gp is defined as the ratio of the total spread (hopping) bandwidth Wss (the span of frequencies over which the carrier can hop) to the instantaneous bandwidth Wd of the data-modulated signal actually occupied at any single hop frequency. Since the total spread bandwidth equals the number of available hopping channels N multiplied by the channel spacing (approximately equal to Wd for non-overlapping channels), this can also be written as Gp = N, the number of distinct frequency channels available in the hop set - a larger number of available hop channels directly gives a proportionally larger processing gain against any narrowband jammer that can only occupy a limited fraction of the total hop set at any time.

In a fast-hopping system, since multiple hops occur within a single data symbol period, the receiver can combine the multiple independently-faded/independently-jammed sub-hop observations for each symbol (a form of frequency diversity combining analogous to rake-receiver combining in DSSS), improving robustness against both frequency-selective fading and partial-band jamming beyond what the simple channel-count processing gain alone would suggest, at the cost of requiring a frequency synthesizer capable of settling to a new frequency many times faster than the basic symbol rate. In a slow-hopping system, since a jammer or fade affecting one particular hop frequency corrupts several consecutive symbols transmitted during that hop, slow FHSS relies more heavily on external forward error correction coding and channel interleaving (spreading burst errors across multiple hops after de-interleaving) to recover from the loss of an entire hop's worth of data, rather than gaining diversity directly from the hopping process itself within a single symbol.

Properties of Spreading Codes and Their Generation

Spreading codes used in both DSSS and FHSS systems must satisfy several key properties: a very low (ideally impulsive) autocorrelation sidelobe level so that the receiver can reliably synchronize (acquire timing lock) to the correct code phase by searching for the sharp correlation peak; a very low cross-correlation between different codes assigned to different users, so that multiple users sharing the same spread bandwidth (as in CDMA) interfere minimally with one another; a long period relative to the data symbol duration, to provide adequate processing gain and to make the transmitted signal appear noise-like to any unauthorized listener lacking knowledge of the code; and balanced statistical properties (equal numbers of 1s and 0s, geometrically distributed run lengths) that make the spread signal's power spectral density appear flat and noise-like across the spread bandwidth, avoiding spectral lines that could otherwise be exploited by an interceptor or jammer.

Spreading codes are most commonly generated using Linear Feedback Shift Registers (LFSRs): a shift register of length m, with specific feedback taps combined via XOR gates and fed back to the register's input, chosen according to a primitive polynomial over GF(2). Such a maximal-length LFSR configuration produces a maximal-length sequence (m-sequence) with period 2^m - 1 chips, exhibiting near-ideal autocorrelation properties (a single sharp peak at zero shift and a constant, small value of -1/(2^m-1) at all other shifts within one period). For CDMA systems requiring many mutually near-orthogonal codes for simultaneous multi-user access, Gold codes (formed by combining two different preferred-pair m-sequences via modulo-2 addition at all possible relative phase shifts) or Walsh-Hadamard codes (derived from Hadamard matrices, providing perfectly orthogonal codes for synchronous systems) are commonly used instead of plain m-sequences, since these code families are specifically constructed to provide good cross-correlation properties across an entire family of simultaneously-usable codes, not merely good autocorrelation for a single code in isolation.

It is worth further noting that in an FHSS system, the frequency synthesizer's hop-settling time (the time required for the synthesizer to switch from one hop frequency to the next and stabilize sufficiently for reliable data demodulation) is a critical design parameter, particularly for fast-hopping systems where this settling time must be a small fraction of an already-short hop dwell time. This settling-time requirement is one of the primary reasons fast FHSS systems, while offering superior frequency-diversity and anti-jam performance, are more complex and costly to implement than slow FHSS systems, which permit the synthesizer considerably more time to settle between successive hops.

Both fast and slow FHSS variants ultimately depend on the same underlying spreading-code infrastructure (PN sequence generation, as discussed at length elsewhere in this examination) to determine the pseudo-random hop pattern, illustrating that the fundamental building blocks of spread-spectrum communication (PN sequence generation and its correlation properties) are shared across both the direct-sequence and frequency-hopping families of spread-spectrum technique, even though the specific way the PN sequence controls the transmitted signal differs substantially between the two approaches.